What is the inverse function of f(x) = 1 + 4x

The inverse function of f(x) is defined as the function
which when applied to the result of f(x) gives x.

Let’s
take f(x) = y = 1 + 4x

Now isolate
x

y = 1 + 4x

=> y – 1 =
4x

=> [y -1] / 4 =
x

Interchange x and y. y is now the inverse function of
f(x) = 1+ 4x

=> y = (x
-1)/4

Therefore we have the inverse function
of f(x) as (x-1)/4.

To verify: f(x) = 1 +
4x

Applying 1 + 4x in the inverse function we have (1+ 4x –
1) / 4 = 4x / 4 = x